Memoir of my Doctoral research endeavour

The big commercial picture

By 1990 TMCP (Thermo-Mechanically Controlled-Processed) steel plates were pouring into Britain from Germany and Japan, and then British Steel had no choice but to buy them and put them through their pipe-mills to make pipe the customer wanted.
Not quite what you want to be doing: paying competitors for their steel when you have idle plate production capacity.

TMCP steels are like a new generation of steel; something of a break from the past. Previously, a rolling mill only gave shape, and alloying gave the various properties including strength and toughness. With the TMCP approach, tiny microalloying additions in a very lean clean composition interact with the rolling process as part of the development of the microscopic internal structure of the steel.

The approach requires large thickness reductions, a significant fraction of the thickness, per pass. At a rolling temperature whose optimisation to structure formation is much lower than the temperature which would be chosen to make the steel easy to roll - something like 950C vs 1150C - blood-red heat vs yellow heat. Not only are the passes reducing a significant fraction of the thickness, but the steel is much stiffer.

Requiring a special rolling mill which is vastly more powerful and stiffer construction than a mill rolling plate at the easiest rolling temperature.

It follows that for TMCP steels, the product form is sheet and plate.
For thin sheet, such as for automotive applications, you can have fairly much anything you want. That's another story.
For thicker plate for pipe, such as 30mm thickness, things get much more difficult and expensive. These plates used in big infrastructure projects is what this investigation is about.

Looking at the steels, they look the same - they arrive black, and rust similarly, etc.
Internally, the microscopic metallurgical structure - the "microstructure" - is very different. That can be seen blatantly on optical metallography of sectioned, micropolished and microetched samples.
"Classic" plate steels have reaction product of carbon and iron making up something like 25% of the microstructure.
TMCP steels have an apparently very simple microstructure of very fine ferrite grains (simply the iron itself).
If TMCP steels become your familiar reference, "classic" "pearlitic" steels appear very coarse with significant proportions of large lumpy second-phase material in the mixed-constituents microstructure; whereas the TMCP steels seem "virtuous" with their uniform very fine apparently single-phase microstructure.

These TMCP mills enabling this result are very expensive. At the time, the German and Japanese manufacturers had established themselves in a market with supply and demand in reasonable balance. Trying to push into the market, suffering all the "learning curve" in the presence of established incumbents, was not going to happen, so no TMCP mill for Britain.

Hence the project was conceived, into which I innocently walked in 1990.

Is there a way of getting the properties the customers demand from a steel coming off a traditional mill?

What are these desirable properties of TMCP steels?

The TMCP steels have desirable properties which customers required as the endeavour to extract oil at ever further, deeper and colder places continued.

What are these properties?

The low-temperature toughness of TMCP steels is expected, by then current knowledge.
It was just about possible to formulate a "super" version of "classic" plate steel to match the strength and low-temperature toughness of TMCP steels. Hence it was worth trying to find what else might be possible...

The reasons for the sour-oil resistance was the subject of ongoing research at the time.

Weldability was where attention settled. Previous established tests for weld cracking resistance could have every variable set to the maximum of severity simultaneously and the TMCP steel would not crack. In other words - the weldability of TMCP steels was so high that previous weldability tests developed for "classic" plate steels no longer worked.

The "lean" composition of TMCP steels would be expected to give good weldability. But not this good. There was something else going on which was not understood.

The project being formulated by the people I was to work with would have very little money and resources compared to the famous work on weldability of the 1960's at The Welding Institute. Just one research student - which would be myself - and a modest budget. So they had to make a good guess where to look for the answers.

The fundamental scientific issue here is the effect of hydrogen in causing steel to crack. Welds always introduce some hydrogen into the weld zone.

A vast amount was known about the effect of hydrogen on given microstructures and compositions. The experiments are very expensive, but the importance across many fields of endeavour, not just commercial but also military, are high, so there is an enormous detailed body of knowledge on that subject.
The feeling was: we doubt the explanation for the unexpected behaviour could "hide" within the extensive and fine-detailed knowledge of inherent susceptibility to hydrogen degradation.

So where else to look?

Very little was known about the movement behaviour of hydrogen in the weld zone of steel welds. Despite the vastness of economic activity in making and applying welds.
The team I was to work with had made that guess - try movement behaviour of hydrogen in the weld zone for the explanation of the difference in weldability between "classic" plate steels and TMCP steels.

The scene was set for me to walk in, bright and innocent, thinking "welding of steels" must be a simple certainty for building to a regular structured career. I wasn't after anything "fancy". I'd leave that to "boffins". Coming from the steelworks, this should be a "mainstream" activity and be right for me...

I had no premonition of the controversy I was getting myself into!

What do we see when we consider hydrogen movement in welds?

So the initial distribution of hydrogen in a weld and how it moves in time is going to be the investigated subject...

OK - so we look at the topic... What is known already? What does general science suggest can be done in this area?

Immediately, we see an abnormal situation.

There is almost no literature on where hydrogen is in welds, and where it goes with passing time. When the issue has central significance across a huge range of economic activity.
Technology for avoiding hydrogen risks means hydrogen must dissipate in time. But detail description of what happens is almost absent. In the context that there are at least tens of thousands of scientific "papers" on how hydrogen degrades the properties of metals, there seemed to be something like four investigations described in "papers" on hydrogen distribution and movement in the weld zone, in all the world, over all time. Good contribution from the Soviet Union - cooperation in welding continued throughout the Cold War :-)

So let's get this straight - each year millions of tonnes of steel are welded into critical structures, and no-one has much idea where the weld hydrogen which creates much of the boundary envelope of "satisfactory welding conditions" goes...!


Well, the scientific difficulties in making such an investigation come into view very quickly, when you start to think about it.

The reported values in the literature for how fast hydrogen moves in steels are all over the place - tens-fold and more of range.
Whatever, you find as a qualitative observation that hydrogen will move millimetres in minutes through steel at room temperature.
The significance of that?

That rules-out the standard method of metallurgical investigation - cut out a sample and investigate in the laboratory what is of interest to you it in the days and weeks following. The sample has to not change in that time.
It's almost impossible to extract a sample from a weld quickly enough to retain the hydrogen you are trying to observe and measure. That would have to be a fraction of a second - without causing any changes or damage to the sample which defeating the point of the exercise.

OK - suppose we could overcome that problem...

What laboratory technique are we going to measure the hydrogen? Hydrogen is element number one - it doesn't have any usable interaction with electrons in an electron-microscope, with X-rays, etc. All the fantastic techniques in a well-equipped Materials and Metallurgical laboratory - all of them are as much use as chocolate fireguard in this case.

That on its own is a "show-stopper".

We contemplate two "challenge" dimensions which kind-of sweep an area in a "product" (multiplied-by) relationship of the "fundamental difficulties" compounding each other.
The reason there is so little information is already sufficiently explained.

Life's experiences so far had already formed my clear strong opinion about the term "impossible".
Something is impossible if it violates a known well-demonstrated physical law of the Universe. For instance; the Law of Conservation of Energy is abundantly observed to always hold, so a path which has that Law violated can be dismissed as "impossible".
Anything else - it can be "difficult", "challenging", it could be "infeasible" if the difficulties and effort required stack up too much. But not "impossible".
Nothing has yet appeared which defines the challenge as "impossible".

It's time to draw breath and think, because these are realities and you are venturing into the unknown.
One good "subtitle" for my research area was coming into mind; "To boldly go where no-one thought it a particularly good idea to go before."
(based on rewording the subtitle of the Science-Fiction television series "Star Trek"; "To boldly go where no man has gone before").

Meeting the sponsoring company

Eventually the day came when we journeyed to the project's sponsoring company, at their large factory. They are a welding equipment and consumables company with a worldwide presence in welding.

Welding consumables include the welding wire which becomes the metal of the welds performing their engineering function. The incentive for the sponsoring company of participating in this project was to be able to optimise their products first. In sharing advanced knowledge of what research was showing must be the way forward in structural steels welding.

Seeing all the product lines being made in this large factory was an exciting "buzz" for me, coming from my steels and manufacturing background.

One addition to the meeting was to go and see "the financial person". Given the explanation that the company had funded several projects from which they had got nothing. I duly offered pleasant comments and mentioned my background in manufacturing.

I soon returned to the factory on my own, meeting another researcher being sponsored at another university. We had demonstrated to us the welding consumable product of most commercial importance to the sponsors. Plus a briefing on the technology of welding, in particular regarding the increasingly dominant "Rutile Flux-Cored Arc Welding" wire product.

So where are we now?

Seeking inspiration, you go down to the workshop, run a line of weld on a piece of steel plate you picked out of the scrap bin, then lower it into a glass jar you have filled with glycerol (a goopy liquid with no preferential solubility to hydrogen). Then contemplate, chin on the desk, as bubbles of hydrogen "fizz" out of the weld.
[OK - it has to be hydrogen - nothing else in the Universe travels that quickly through steel. It's way out there on its own for movement rate through steel by orders of magnitude. Analysing and proving it's hydrogen would cost too much]
After time, you start to see bubbles of weld hydrogen emerging out of the back surface of the plate, opposite to the weld.

That hydrogen has just travelled through 10mm of solid steel in a few hours.
Get your mind around that!!!
The steel still has say 355MPa of strength and no other change. No damage, no cracks, nothing.
Soon you are seeing quite a lot of bubbles forming on that back surface. Eventually they start detaching from the back surface and float up in the glycerol, as they become big enough for the buoyancy to detach them.

Every atom of that hydrogen has just made that journey through 10mm of solid steel.

You are seeing hydrogen gas on the back surface.
Now, hydrogen was not in this molecular state as the gas as it passed through the steel...
It can't be - it "blew" through the atomic crystalline lattice of the steel where the "slinking" has to be through free spaces similar to the size of individual atoms.

So in what form is the hydrogen within the steel???

When you start sketching a section of the plate-with-weld and labelling-up all the things you don't know about or have queries regarding, your sketch gets rather highly annotated...

Gift of some steels - a blessing beyond anything I comprehended at the time

I went around to then British Steel research laboratories in a van, and one of their metallurgists, one of those who I was later to realise contributed a lot to the "let's look at hydrogen distribution and movement in steels" guess, loaded me out with five different plates of steel. Only one was a British Steel plate - the "classic" plate steel. The others he'd kind of "hidden under his raincoat and smuggled out" - large offcuts of various German and Japanese TMCP steels.

It was to be a couple of years before I realised what a gift he'd blessed me with.

What happened next?

Sadly, the reality was the project went into melt-down.

No idea for starting and developing the project seemed to find any liking.

An elderly very leathery-skinned metallurgist rated as "a smart bloke" had shown and leant me "Welding steels without hydrogen cracking" by The Welding Institute.
What with this and other readings so far, I began to formulate some provisional plan.
When in my mind I laid things out in a sequence, there was a "big one", looking to be the most vital and also the biggest challenge.
Whatever is inferred from any other data which might be generated, the "big one" was this: we needed to see first-hand, directly, where the weld hydrogen is at the moment the weld is completed.

There is this expectation from scientific thinking applied by a technical specialist knowing welding. If "nothing additional happens", the rapidly swirling weld-pool, driven by various forces electro-magnetic, surface-tension, convective / heat-driven, etc, should mix weld-hydrogen, understood to enter at the weld-pool surface where impinged-upon by the intense welding-arc-atmosphere, pretty uniformly through the weld-metal.
But does "nothing additional" happen? We need to know.

If you had direct observation, you could organise other experiments "before", "after" and "around" that stage, which would together give a good useful portfolio of experimental information.

Coming from a steelworks and technical background, including things like maintaining my own motorcycles when a youth, I looked to methods which come from workshop knowledge and skills.
I visualised a technique where the sample is obtained by machining from a weld while the weld is kept at liquid nitrogen temperature. Which is -196C. That's 2/3rds of the way to absolute zero from room temperature. Which is seriously cold and in the domain of "cryogenics". At that temperature, hydrogen in steel becomes immobile, attaching, with some likeness to condensation, to microscopic features and irregularities in the steel.

There is a "rule" it seems generally necessary to follow. If a path has a difficult stage which may or may not work, you need to test that stage first. In order to know whether the whole plan is a "go" or a "no-go". The liquid nitrogen temperature machining idea had that property; it was an unknown which may or may not work. So I had to do a proof-of-concept test.

The idea was considered on its merits in the machine-shop of that University Materials department. I nominated a machine-tool, an obsolescent type called a "shaper" with a simple tool and no bearings or complex mechanism near the tool.

The plans where developed in consultation with the machine-shop for a proof-of-concept rig which had no weld-sample, and served no purpose but to test whether the cutting happened as desired. Given all the cutting would ever do is machine away part of the test-rig itself.
The complete unknown, even after consulting a local tooling company of worldwide repute, was how the tool would react to being driven into a cut when the tool is at liquid nitrogen temperature. We had to be prepared for it to shatter, with some elastic energy sending bits flying. The reason for a low-stakes quick proof-of-concept test. With the rig complete, liquid nitrogen was poured in, the machine-shop was cleared and, crouching behind the machine in helmet, visor and padded clothing, I pulled-over the clutch-lever and let the machine stroke once. Gathering around, a cut had been made, so everyone retreated again and I pulled-over the clutch-lever and let the machine keep stroking, with the auto-feed on. With the cut completed, we gathered around, and found machining swarfs filling the bottom of the rig and a smooth machined surface. The tool seemed fine. It was clear that the inherently brittle cutting tool material is as brittle as it can be by room temperature, and freezing it has no further effect. Another layer of test cut and it was concluded that the method behaved benignly. Work resumed in the machine-shop.

There has been a recurrent theme in my career and this was one of the occasions where such an auspicious event was to occur. The metallurgist who is considered "a smart bloke" came down the steps of the machine-shop. His steps faltered to a stop as he came to the floor, wearing an expression of some incredulity, as he observed me with machine-tool going and low-temperature "steam" pouring off the test-rig. Commenting "I'm machine steel at liquid nitrogen temperature" he replied "I can see what it is you are doing! I can't believe anyone would actually do it!!!". Knowing my research area, he had comprehended in entirety at-a-glance what I was trying in order to get to the "secret" of where the weld hydrogen is.

I'd had one of my big learning experiences in the course of this trial. I mentioned a local tool company. The machine-shop had insisted I talk with a tool company. I was braced for them to say incredulously "You are intending to do WHAT???" and slam the phone down. On the contrary, the pause was followed by a considered "We don't know the answer to that. You need to speak with our chief metallurgist. He's on business in Europe now, but will be back on Monday. We will tell him you will be calling him".
I learned it is remarkable what can be achieved calling organisations you have never met before, introduce yourself and introduce the topic which leads you to call them.
Back to the unfolding story of the project...

The application of the technique was going to have to wait, as when my research supervisor arrived, I overheard the experienced metallurgist ask him in a rather loaded tone "So now then who is <...>?". The omitted word was not flattering.
1~1/2years in - that was the breaking point. I omitted saying that while the time-served machinists in the machine-shop had looked at the idea on its merits, the same positive outlook could not truthfully be reported for the project supervision. Relations with my supervision had probably already been strained beyond recoverable when I slowly enunciated "I am going to get up out of this chair, and walk towards the door, and if by the time I reach the door you have not proposed an alternative workable idea for a line of research, trialling of this liquid nitrogen temperature machining idea, in support of the research proposal I have outlined, will be implemented."

So I now had a way to observe the location of the weld hydrogen at the moment the weld is completed. As it seemed a reasonable leap-of-faith that I could produce a more sophisticated rig which held a weld sample. Enabling me to machine so that the weld section I wanted to examine was presented with the weld hydrogen still "frozen" in place. Some investigative method must be able to show where the hydrogen is. Of which the likely one would be that low-tech favourite - watch it bubbling out into glycerol. Return the sectioned sample rapidly to room temperature, do something with glycerol, and observe where the weld hydrogen bubbles out of the new surface. Revealing where it had been in the original volume...

Now I needed a "lifeboat" - an organisation which would take on my research - in order to save myself.

Moving hosting research organisation

I had nothing to lose. Venturing forth with my entire future hopes at stake, I found an organisation which would host me and my work.

Something which was clear in my mind - this was "blood on the carpet", and life in future was going to be tough.

Getting thoughts going at new hosting University

The Professor (UK terminology) heading the Department talked me through some "general concepts" when approaching issues framed as diffusion (of solutes in a solvent material - in this case hydrogen in steel).

About the concept of "diffusion" - look on-line or at my thesis at the Brunel University archive with its review of literature on the subject.

A lot of mathematics is on offer on this topic. "Keep it at arm's length" - for reasons which will emerge in the story later.

The Professor did make this prescient point: Fick's model and his Laws represent what might happen at an atomic or molecular level; but beyond that the vast amount of mathematics "solving" Fick's 2nd Laws to predict where the solute is at a given time in the solute material are mathematical "shapes" with no physical significance.
OK - if necessary take it on trust that this distinction is important.

For all the mathematics presenting itself or willing to absorb all attention, I was looking for something I could work with practically, and I went away with one thing the Professor pointed-out to me. There is "an equation", ie a mathematical prediction, for one characteristic of diffusion which looked usable to me. If at zero time there is a region of a body which has all the solute and the rest of that body has none, the furthest "frontal" distance to which the solute will have spread in elapsing time obeys the relationship
maximum_diffusion_distance = 3.91 x square-root(diffusion-coefficient x time-elapsed)

Let this be known here as "the distance in root time relationship". Sometimes even more abbreviated to the mathematical formulation "x vs root-t".

It seemed likely the hydrogen going into the weld from the arc is in-or-around the weld as just made. The plate metal has essentially zero hydrogen to start with. The physical model which the mathematics quantifies and the physical situation of the weld seem to match.

As ever, you have to be careful with your ideas and not jump too far in assuming what actually needs investigating. At least there's an idea forming of an investigation where observations can be offered alongside an expectation coming from physical laws.

Its potential advantage is that you only need to detect whether hydrogen has arrived at a presented surface yet; not concentration of hydrogen at location-in-volume profiles - which is quite infeasible.

Once again we are connecting thoughts and it involves glycerol.
We look at a surface and see no bubbles, then after a period of time we see bubbles starting to form. At which moment the "hydrogen propagation front" has travelled the distance from source to that surface.

Getting going again...

Firstly - let me confess I've taken a slight liberty with the actual chronology of something previously mentioned. Only in the conducive environment of this new University did I sketch a cross-section of a weld upon a plate then annotate it with all the physical questions I could visualise.

Here I am with "a clean new start".
With mentally stimulating guidance, I've absorbed a lot of literature on the behaviour of hydrogen in solution in metals, and my head is now well loaded-up with observed behaviour and explanatory theories.

Already, I'm reading there's odd things about hydrogen diffusion in steels, which could be "coming-in" in making any experimental programme "interesting". One gathers one's strength in preparation, looking forward...

Here's another vital step on my path which I am going to share with you. Be careful though - this thinking could disrupt your life :-)

Using figurative imagery: when stepping into the unknown, you need to know that where you land your steps are solid ground. Get that wrong trying to walk across boggy ground and your foot and leg disappear into the mire, with yourself probably falling face-down into the mulch.
In science, if you wrongly take as reality something which proves illusory, you will also tumble. At worst, you get some apparent pattern and waste time going some distance up a pointless route. That could break a person. More likely, you will expend effort refining your experiment but never get any pattern in results, before the realisation comes that you have pursued a false "lead".
Alternatively you could "get lucky" and yourself stay in ignorance, no-one else spots the fallacy and you get to publish something which looks impressive but is fundamentally wrong ("the Professor's prescient point" about "the mathematics of solving Fick's 2nd Law" relates to this fault). Very shortly you will find the "just because it is written doesn't mean it's real" warning...

You do need to take advantage of existent knowledge, to launch off into your research on something unknown, from as far forward as you can. In order to make maximum progress. But how far forward is the knowledge? Just because it's written doesn't mean it's true.

Another way of constructing an analogy is to consider constructing a building. It needs firm foundations. A fixation on the grandeur of your design succeeding in diverting everyones' attention from absence of foundation will not coerce that your structure if you attempted to build it will defy gravity and stay up lacking foundation!

Considering everything I had read (a lot) and what I had observed (a little); I discarding anything which did not have self-evident readily-observed proof. One quickly pruned back to this starting-point: solute hydrogen does move around in steels with elapsing time.
That is not a very far-forward starting point!
Huge amounts of literature are considered, for sure, but are set-aside due to a nuanced evaluation of their reliability.

An example of what we can trust are Laws like the Conservation of Energy which is observed to hold so generally that it is one of our "safe footfalls" as we probe forward into the darkness. Laws like Newton's Laws of Motion are found to be incomplete in that Relativistic effects identified by Einstein need to be appended; however in common experience that "shortcoming" is often less than negligible, while conditions causing the additional behaviour to emerge are well-known and can be identified, so Newton's Laws are another "safe footfall". These are some of the foundations of science we learn at the start, as children, in school.

An example of an immediate "casualty" are Fick's Laws. Fick himself, back in the 1850's, knew his model was a "baseline" requiring none of a number of things which will certainly occur - such as preferential interaction (neither "attraction" nor "repulsion") between solute and solvent - to occur at all. So for constructing scientific research, Fick's Laws are anything but a safe foundation which can be uncritically accepted as reality.
I was also correct regarding the "Devanathan and Stachurski electrochemical hydrogen permeation cell", which looks like a panacea for measuring everything about hydrogen movement in a material. Later reading lead to a mind's-eye vision something hybridising a tidal quicksand like Morecombe Bay with The Sirens of Homer's "Odyssey", as a place of doom for those pursuing engineering answers through scientific measurement.

Here is where the warning is delivered strongly. To be a good scientist you need to question what is "real". However most people need "certainty" in life and many will react furiously to a nuanced answer in regard to something which is written as fact. They have a vision of a "one-way valve" - once something has been written as fact, that establishes fact and administrative actions can use that to coerce events to conform accordingly.
I came to this realisation: a lot of being an investigative scientist is about being able to function effectively while so little is known.

Time to do experiments

I need to do experiments.

I started with a "scattergun" approach, in which I made fixed closed-ended allocations of time and effort to different trial experiments. An ulterior motive was to have missions which introduced me to my new hosting research institute and its staff.
Some experiments tried to replicate experiments which yielded the seminal contributions to knowledge on hydrogen in steels behaviour.
My Thesis section "Unsuccessful experiments" (pages 99 to 107) describes some of these. A reality of science - just because an experiment worked before doesn't necessarily mean it will work now. Logically, the experiment must have worked, because the knowledge gained from the experiment(s) did not exist previously, and those findings have been repeatedly found correct since. The reasons why the historical experiment would not replicate now might prove a project in itself. Speculations might take the form "Perhaps acids were less pure then, and contained some impurity which enabled the reaction to run then as described, which will not happen now with today's reagents?".

Other trials didn't produce anything useful and were tenuous ideas anyway. Which would make them even more time-consuming to describe - and you could never explain and justify to a non-scientist anyway. About casting far-and-wide, trying to make your own good luck. So only by looking in my lab-book could I find note of some ideas tried.

So for about 3 weeks I was going about the department in a flurry of activity, appearing here, there and everywhere, pursuing ideas.

Something it would be really useful to know is the diffusion-coefficient, "D", for hydrogen in the steels I was investigating.
The "unsuccessful experiments" in the "scattergun" trials program of experimental methods had denied me a route to this information, so far.

Why not simply look up that value in the literature? The diffusion coefficient of hydrogen in steel...
Not useful, because the reported values spread over a wide range - as previously mentioned. Unusual, but that's the case.
Whatever; we can "get on the learning-curve" by measuring our own value of "D" for hydrogen in one of our plate steels.

One problem is: what hydrogen source are we going to use to provide the hydrogen whose passage through the steel is the subject of physical measurements revealing "D"?
We don't want the front of the building lying in the forecourt (hydrogen gas as a hydrogen source), nor half your colleagues deceased in a poisonous-fumes mishap (you used hydrogen-sulphided acidic solutions). Electrochemical methods - I'm not a chemist, mastering them would be an entire endeavour in itself, and they tend to introduce complex extraneous characteristics which obscure the physical characteristics we wish to observe.
The "unsuccessful experiments" mainly comprised those trials where hydrogen sources of limited hazard and complexity described in the literature failed to be hydrogen sources at all for this experimental programme.

In summary; there isn't a safe or cheap, let alone safe-and-cheap, source of hydrogen for conducting hydrogen diffusion experiments in steels.

So what hydrogen source for our experiments are we going to use???!!!

Emerging from this "fog" of desperation about hydrogen sources is the realisation that only a deposit of weld metal offers a cheap safe hydrogen source for investigating hydrogen movement behaviour in steel...

How useful can be a weld deposit on the steel whose properties regarding hydrogen movement in it you want to investigate?
It doesn't look like an "equipotential source"; where a hydrogen source maintains a constant hydrogen concentration at an "entry surface".
Hydrogen concentration in the source will deplete in time as the hydrogen escapes from the weld deposit surface and disperses into the substrate steel whose properties to hydrogen dispersion we wish to measure.
It would be a mistake to get "hung-up" about this "shortcoming" we can perceive, as we don't know anything yet about what really happens and what the priority issues will prove to be.
Best let the approach give us what it gives and the re-evaluate where to go next when it has delivered what it can. Experimental science is like that. You often don't get gifted "premiums" and "ideals" to work with.

So I entered into a time of deep fundamental contemplation of the overall matter.

In my mind I "juggled", "superimposed" and "slid by each other"

looking for where Nature grants a "window" through which the movement behaviour of hydrogen in steel can be observed and measured.

Sliding these thoughts around, suddenly I saw a "lining-up" which did appear to offer a "line of sight" into hydrogen movement behaviour in steel!

My practical background coming from the steelworks and workshops gave me the special advantage to see the opportunity. Without the "workshop techniques" layer of the sliding-past of ideas, the opportunity would not have presented itself.

The method uses a machine-tool cutting to present a new angled surface at the rear of the sample on which the weld-metal hydrogen source had been deposited. Angled in the sense that along the length of the deposited weld the hydrogen is presented with a graded increase in distance from the weld metal deposit to the back surface. A wedge shape.
We've already introduced "the distance in root time relationship". Our premonition that it might offer an experimentally manageable approach to investigating hydrogen movement and possibly estimating "D" is looking like it is going to fulfil.

Immersed in glycerol, the "wedge" sample should show a "carpet" of hydrogen bubbles on the rear surface, initially at the thin end and "advancing" along the sample to increasing thickness of sample in elapsing time.
Know the time the weld was made, the experimental observations would be how far along the sample the hydrogen has advanced at a succession of increasing elapsed times.
These can be processed into the propagation-distance vs elapsed-time data-points which are plotted ("graphed").

If the "the distance in root time relationship" were correct, the recorded results plotted as "propagation-distance" vs "square-root of elapsed time" would be a straight line.
That's a "qualitative" relationship. If you see some straight line, the expected behaviour derived from the underlying theory is, at a minimum, very likely at least a significant part of the explanation of the actually behaviour. To be misleading, something else would have to systematically produce that very characteristic qualitative linearity of distance in root-time.

We can go onwards to a "quantitative" relationship.
If there is a straight-line portion of that graph, from its gradient (slope, tilt), you can then extract by a simple calculation the apparent diffusion-coefficient "D".

Magic! :-)

Of course, we don't really expect things to work so perfectly... We are going to get a messy cloud of results... Maybe only a bit of a trend to a straight line over some of the root-time axis length... With the graph drooping-off, disappearing into a fuzz of unclear results. etc. Being realistic, yes??? For a start, the hydrogen source is depleting and of reducing concentration throughout the experiment...
But let us at least see what happens, as this is the best concept so far, and expending further mental effort prejudging the outcome would be wasted effort.

The machining mentioned to form the inclined back-face has to be done after the weld is deposited, as the weld heat would raise the temperature of the thin end very high. Producing various non-uniformities and changes we do not want.
Given we already know that hydrogen can propagate a millimetre through steel in minutes, we can see that that machining operation needs to be fast. That could prove "interesting" on a practical level ;-)

Seeing Figure 2.5 on page 56 of my Thesis is jumping-ahead to the fully-developed "WWHP test", but at-a-glance shows the overall nature of the first test about to happen.

Anyway, I've got this sample in a glass instant-coffee jar filled with glycerol, and am taking an extended tea-break while occasionally writing a note of where the hydrogen bubbles are emerging. Not expecting much, you know...

Things didn't quite work as expected, as my first effort at "a very very rough estimate" delivered and then some!

The results graphed are presenting on page 143 of my thesis as Figure 4.1 - the "W9590NTR" points in red (the other points in light-blue were from an additional non-plate steel - just to check the method works for a range of steels).

The striking feature of the results which leap out and almost knock you over backwards is that if {thickness of sample through which the hydrogen has diffused} vs {square-root of elapsed time since the weld was deposited} is plotted, that graph-line is quite straight over a long range. The very linear trend from "60" to "150" in root-seconds corresponds to 1 hour to 6 hours elapsed since weld completion.

"Perfection" like that is not expected, especially from such a trivial effort.
Perhaps credit that there's some seriously good mentoring going on which has systematically tipped the odds in my favour.

There's something my mind had at its centre: "How can a depleting hydrogen source 'push' a strictly model propagation-distance proportional to root-time relationship, especially over a long time-span to long propagation distances several times the source thickness, and width - particularly when there is the immediate surface of weld bead for the hydrogen to freely escape from so it looks unnecessarily hard work for the hydrogen to push its way into the underlying plate metal???"

My thoughts benefitted from the logical structure provided by the majority scientific method of "hypothesis testing". That training and structure is making me think "Why is the distance in root time relationship so perfectly manifested when there are so many uncertainties?" and "Do we really believe an initial finite hydrogen source about 3mm thickness and 14mm width can push hydrogen through 15mm of plate steel?".
See thesis Figure 3.3 on page 117 for some measured weld cross-sectional shapes and dimensions.
If most first-assumptions including "Fickian" behaviour applied, hydrogen concentration would drop to zero in the first instance at the weld-deposit free "top" surface, given hydrogen would be assumed to be a "freely volatilising" solute, and remain "firmly anchored" at zero for all subsequent elapsed time. "Driving" a rapid escape of the weld hydrogen "down" the steep concentration gradient to that surface.
Whatever - we now have some serious questions stacking-up right here at this early stage.

Anyway, looking onwards from what we have for now; which has so much qualitative order that something physically fundamental must be exercising significant control of at least part of what is happening...

Things from this point got even better.

I have my first significant interaction with my new supervisor and things get even more good

My new supervisor now has his first interaction with the project, applying his extensive welding-with-science knowledge and experience - and almost unbelievably, things get even further better...

My new supervisor is looking at that first "wedge" sample, now out of the glycerol and cleaned after completion of the weld hydrogen movement observations. Turning it around in his hands, looking at it from various directions and contemplating it and its significance.

This is what he had to say.
"I like this experiment very much, because it tells you several things from one experiment. Which is much better than several experiments to measure one thing."
I pondered extensively about his comment, and the way he contemplated the experimental sample for such a long time, looking at its weld-face, the newly presented back-face at the wedge-angle, side-on and end-on.

The meaning came to me transposed into my own language and way of expressing things.

Everything in my experiment matches what exists in a real weld. Therefore, whatever my experiment does matches what a real weld will do. That is very significant, because any observations and data the experiment provides, processed and interpretted, applies to a commercial weld. Nothing the experiment does can be misleading, because it is a weld.

This point explained in a bit more detail...
That my "weld" doesn't weld anything to anything else doesn't matter in this case. The steel tested and the weld deposit can be one-and-the-same as those used in the commercial situation. Furthermore in every metallurgical sense my "wedge" test and a commercial structural weld are identical. For example, the effect of the weld upon the plate metal - such as the local effects of the temperature-cycle of the weld - is identical in both.
Everything of the commercial weld is replicated in the "wedge" experiment, and nothing extraneous is introduced into the experiment risking introducing spurious effects into the data.

There were some practical details I had to get right to make the scientific and metallurgical match perfect. In taking my crude "wedge" test and developing the "weld-wedge-hydrogen penetration" (WWHP) test. See page 52, section 2.3.2 "The standard weld sample" and page 54, section 2.3.3 "The WWHP test".
The main requirement was to make the sample appear to come from a large plate of the steel regarding weld heat dissipation; hence the temperature cycle it experiences. In the standard minute of cooling after completing the weld, the weld heat will conduct far beyond the 15mm half-width of the standard sample. "The standard weld sample" thermally connects to a heat sink until after the cooling period.
Making the handleable "standard weld sample" metallurgically identical to a weld upon a large plate.

The success can be judged from thesis Figure 4.3 on page 145, where six identical samples of the "classic" plate steel have the "WWHP" test done on them. The results have little spread.
The heat-sink of the standard weld sample must be working consistently, as the graph lines extrapolated to zero time (the left-hand graph vertical axis) all have about the same intercept at about a millimetre. Which is about the depth the weld penetrates into the plate surface, placing the weld-metal to plate-metal interface at about that location.
This is all looking fantastic!

The "standard weld sample" can be used in more than one experiment; noting that we have the liquid-nitrogen temperature machining method awaiting application. Giving results which can be compared, coming from a "standard sample"...

Applying the WWHP test to our steels

I prepared "WWHP" test samples from the four steel plates gifted to the project - one "classic" plate steel and three TMCP steels.

It's something of a wild guess to do this, but we have had a lot of good fortune finding the "WWHP" test, and we now had to invite the Universe to reveal to us what it will. Not knowing what that might be...

The results, presented in Figure 4.2 on thesis page 144, "jumped out at us" again.

For the same steel, the results have little spread. However, between different steels the results are very different.
The difference in the slope of these graphs represents a difference in hydrogen diffusion coefficient in steel "D" of more than a factor-of-3 (ie 3-fold; x3).

This was an astonishing moment of triumph for the project. We have found a "window" Nature granted us to look into what the hydrogen does moving in the weld zone, and these results are previously unsuspected.

Instead of "a diffusion coefficient for hydrogen in steel", we find that "D" takes different values seemingly dependent on the nature of the steel.

The findings so far established our research group amongst other research groups also looking at hydrogen behaviour in welds.

Problems recur in the project

The sponsorship research budget was not invoiced onto the University!
Without money, my research was brought to a stop, as I exhausted all the things I could do without money.

Had the sponsorship money been "within" the University, several persons could have signed my expenditure requests - my supervisor, the Head of Department and the Deputy Head of Department. No-one could orchestrate to "block" the research. Conniving schemes would not happen by reason that they could not be effective.
In this different situation with the money parked at the sponsoring company, there was no way I could get at it.

What was my supervisor doing? He didn't seem happy, and talking with him on the matter produced no result or explanation.

After what I had been through with the first hosting organisation for my research, I was incredulous that a similar malady was happening again.
Something malign had followed me from one institution to another - but what?

The funding was the big bad problem, but I was also hearing from my supervisor that there were reservations that research direction including the "WWHP" test was the right approach. !!! A mystery! We have the success of finding that there are important differences between steels - seemingly fulfilling the suspicions at the start of the project - and we were making progress in an area where almost no research had previously been achieved.

Once again, I meet a juncture which defines that a strained relationship exists.
In one of the periodic project reviews evaluating whether the research should continue, it is being put to me that the absence of recent progress was due to inability.
Pointing out that my funding is being withheld would be politically insensitive and also pointless, as my supervisor full-well knew I was being denied access to my research funds.
I assembled technical reasons for the pause after the initial flush of progress, politely skirting around the funding matter.
Handed the appraisal form with an instruction to sign it, what had been written was what had previously been contended. Signing it would have been equivalent to "signing my own death-warrant". I handed to form back stating "I am not signing this".
I calculated that made all the problems theirs, as the research funding was now months overdue, and the procedure to abandon a project would find this. What was being done was certainly against the interests of the University, so I could be sure that despite seething resentment the matter would stay within the Department.
My calculations seems to have been overall correct and we found a way to deflate the pressure from the situation.

I also calculated that, with so much time having gone by, if I went wearing an expression of innocence to the financial office asking if my bursary had arrived yet, the irregularity would get notified to the top of the University.
Indeed, the effect was a forceful response of the University leadership upon the Department, who had to advance all money to me immediately from their own funds and an order to get the sponsoring money invoiced immediately.

All I was interested in was a well-run successful research effort - so my only question was "What is happening which is causing all this?".

A change of Head of Department happened in the normal course of succession and rotation, bringing a different style and in the course of efforts to "set things straight" the explanation was found.

Miscalculating loyalties, the miscreant revealed himself in a large meeting looking at the future of the project. That was lucky - I "played a hunch" and everyone senior in the Department graciously agreed to come to this meeting I organised. Faced with "so many senior people to influence" the person thought he had the stage where revealing his true views and actions would be right.

Events at both my first and second research establishments had one common explanation. The point-of-contact at the sponsoring company, their senior technical person, had some very odd beliefs about managing people; also some very poor ideas about how science works.
He had been saying different things to different people. With the effect that it set them on collision courses. Each being unable to work out "why the other party seemed to want to wreck the project". Each had talked directly to the sponsoring company, so we each thought we knew the sponsoring company's true wishes.
The "poor science" was in what he thought was "the way to the answer".
Which drove his ill-judged manipulations of people in the project.
Yet another aspect of his views was revealed, about how the project should get its driving force. As in the general case of single-objective projects, it would be expected that the recruited researcher would drive the research. Mentored by the hosting University. This person believed that "the University" should provided the ideas (a nonsense - only the specialist taking-on the research area can know its intricacies). Hence the mystery of the "1~1/2years no liking for any ideas for a research programme" at my first University was explained. For every research idea they went to him with, he pronounced an unfavourable opinion, visualising that he was awaiting "the ideas of the University" (sic.). In effect, he visualised that he had signed-up for consultancy from "the University" and its academic staff, and was "ensuring" he got that.

He'd been doing likewise to my new supervisor at my new hosting University. Hence the state of the guy.
The sponsorship money left unclaimed at the sponsoring company became explained - my supervisor had been prevailed-upon, taunted to "show strong leadership" and "show himself to be in command".
In furtherance of that belief that "the ideas must come from the University" (sic.).

The early scene at the sponsoring company where we had to file in and meet "the financial person" regarding "We've given money to projects and got nothing in return" was also explained. This person at the sponsoring company was doing the same nonsensical manipulations to every project formed with a sole researcher.
When I later emerged from my project, I was thought to be "the sole survivor".
I was later discretely told by others working in steels and welding that "word had got around" that this person representing the sponsoring company got a reputation for being "strange" and that people were avoiding talking with him. Whilst he apparently offered the money of a large company, he seemed to cost organisations much more from trouble than they received in sponsorships.
I was seeing two sides to the story, as sponsorship had got me through more education to make up for an imperfect performance at my "first Degree" (Bachelors Degree) level. Also getting me started; my first mentoring on technology of welding; getting "energy" from the size of their busy factory operation then in North London; experiencing my first weld tests and getting some experiments done using their hydrogen measuring equipment.
I conjecture that the fellow, having studied at a large extremely prestigious University, carried that as his image of what an academic institution should function like.
We humans are very fallible, and I can see how someone could easily make these mistakes.

All this left me with a severely mangled supervisor who none of us knew how to recover in any immediate way.
To compound this, it was to transpire that he was developing the ailment of "multiple sclerosis"; yet to be diagnosed. These early first effects before the diagnosis tend to be include struggling, frustration and anger.
One credit I granted to myself was that in defending the project, I had never done anything beyond what was absolutely necessary to protect the project. That made a later reconciliation with my by-then ex-supervisor possible.

The events had certainly done me significant damage, as the progress, continuity and forward momentum of the project had been disrupted. Future funding and support would affected, and I had to rebuild the programme and make it "a force to make way for" again.

I was also left chagrinned, as it seemed that the answers are with the steels, and the first University I had taken the project from was expert in steels.
Nothing could be done about that. The reality was my new University had made the progress possible which had me alive and well, looking at this vista.

Strongly dismissing bad science

The person leading the sponsoring company's technical activities had mentioned his "partition hypothesis".

It was barely noticed because it is was barely probable.
"Occam's razor" is often illustrated by the "tiger" example. If within a building you go to the door to the corridor and open it, and you do not see a tiger sitting there, the simplest explanation is that there is no tiger. Without any proof, you are dismissive of the explanation that the tiger became frightened when it heard you coming, and hid around the corner, so explaining that while you do not see a tiger, the tiger exists. The reason you are dismissive of this explanation is that it is implausibly complex.

The "partition hypothesis" suffers the same dismissive instinctive sentiment. It is described and analysed in my thesis pages 37 to 42.

Essentially, the hypothesis attributes en masse bulk transfers of weld hydrogen to a driving force which good analysis reveals is quite small, and completely ignores the "kinetics" - the rate at which things could happen and need to happen where energy makes something possible.

The "WWHP" test results already performed showed an overall "picture" which excluded this hypothesised mechanism, if it were happening at all, from being more than a negligible effect.
The evidence so far (and subsequently supported) is that hydrogen simply "spills out of" the weld bead in a dispersive random process. Essentially, it's increasing "entropy" . Going from an ordered state of all hydrogen concentrated uniformly(?) in the weld-deposit to an increasingly entropic state of the hydrogen dispersed across the volume of the weld zone, flowing "outwards" "down" concentration gradients.

Focus on the primary commercial goal helps "scale" scientific concepts so priorities fill the view.

Getting moving again - rebuilding after the interruption

The "WWHP" test series was applied to more-commercial weld systems. The highly-productive semi-automated Rutile Flux-Cored Arc Welding (R-FCAW) became the test weld for the remaining experiments.

The results from the later experiments confirmed what was emerging in earlier experiments.

A fluke of good luck gave us yet another variable, weld hydrogen concentration. The sponsoring company changed its production method for the R-FCAW, lowering its hydrogen potential without any other known change - so the last of the previous "line" and the first of the new "line" were provided to us.
The effect of that variable was good to demonstrate and know. The hydrogen level in the weld proved to be not a big variable on results obtained; a valuable finding.

These results are presented as graphs in thesis page 146 Figure 4.4 to page 149 Figure 4.7.

For detail and analysis, it would be necessary to read my Thesis, which has been commended. Broadly, having got practiced at the "WWHP" test and refined its implementation, I produced a goodly portfolio of results. With a lot of evidence of excellent consistency; therefore trustable accuracy. Truly excellent, given the situation as the project was set up.

It's clear we need to be get the "liquid nitrogen temperature machining" applied now to "the standard weld sample". In order to get that direct observation of where the weld hydrogen is at that zero time when the weld is just completed. The "WWHP" test results are extrapolating to zero time and giving inference of where the weld hydrogen "front" is at zero time, for whose features we can think of plausible mechanistic hypotheses. However, we need to minimise speculating and get "doing" for best effect.

Before that - let's very clearly register this clamouring perception. It was previously mentioned - should the relative small single "run" of weld be able to "push" hydrogen through up to 15mm of steel?

With a very low hydrogen concentration in the newer R-FCAW wire, it was seeming quite incredible that weld hydrogen should be "pushing" through 15mm of steel. Keeping a linear "x vs root-t" all the way!

I had a suspicion that hydrogen is "preferring" to remain within the weld and "ignoring" nearby surfaces offering it a fast exit from the weldment.

I'd found in the literature an essentially similar experiment, performed a few years previously in 1988 in Norway by the researchers Christensen and Evans. They measured how much hydrogen came out of the back surface of a weld sample, opposite the weld. The experiment is described and illustrated in thesis section 2.4.4, page 82 and the subsequent few pages.
They hadn't managed any analysis of their results (very unusual for a published scientific work, but very understandable in this case). However, looking at these results there was this same thought - according to all current theory, should it really be possible for a single run of weld as the hydrogen source to 'push' so much hydrogen such a distance through the plate steel?

Answers to this were going to have to wait.

Deploying liquid-nitrogen temperature machining to directly observe initial weld hydrogen position

Thesis section 2.3.5 "The sectioning test", pages 61 to 64, describes and illustrates the implementation of the liquid nitrogen temperature machining technique to "the standard weld sample". A surprised Italian conveyor-belt salesman provided from his briefcase the sheet of paper to sketch my inspiration for the insulated toolholder when it came to me on a train journey. The rest of the design was fairly self-evident and simple. Polymer has about a 200th of the thermal conductivity of metals, so small interposed thickness "breaking" all metal-to-metal heat conduction paths has great effect.
Offering a lesson from experience: in the general case of trying to design an experimental technique - or any other "device" - it must have the elegance of simplicity. If the design grows ever-more in complication, you need to abandon it. When a concept or feature "collapses" many layers of complication to a very simple elegant design, you have probably found your answer.

The method applied to reveal the location of the weld hydrogen at zero time when the weld is just completed is sketched in thesis Figure 2.10 on page 63. The experiment in action is shown in photographs, thesis Figure 3.7 on page 131, with matching illustration Figure 3.8 on page 133 offering explanation of what is seen.

The results have a clear pattern. The higher the plate steel hydrogen diffusion coefficient "D" as provided by the "WWHP" test, the further forward the hydrogen front was at zero time of weld completion. That accords with a mechanistic postulation that hydrogen manages to disperse a small distance out of the weld metal beyond the fusion-boundary in the time the weld is being made. That is a very simple concept and fits well with "Occam's razor".

The "WWHP" test extrapolation inference of location of the hydrogen "front" at zero time and the single direct observation of hydrogen front location at zero time using the liquid nitrogen temperature machining method closely concur.

For all practical purposes what is show is: the weld hydrogen is within the weld metal at zero time.
All interpretations are simplified and given confidence by this proof.

That very neatly brings to completion the main experimental programme on weld hydrogen movement in the weld zone.

What can we summarise at this point?

The reasons the project was created were described at the start of these memoirs. How far have we gone towards fulfilling its goals?

We have created a way to accurately measure "D", the hydrogen diffusion coefficient in steel, and obtained accurate values for "D" for a range of plate steels. We find there are significant differences in hydrogen movement rate. Which does confirm the initiators' suspicion that the properties to movement of hydrogen in the new TMCP steels is significantly different to that of "classic" plate steels.
It does seem that weld hydrogen simply disperses in line with entropy, and doesn't do anything spectacular and orderly in line with a thermodynamic driving force.

What does all this tell us about why the large difference in weldability, as in the resistance to weld cracking when large "engineering load" stresses are applied to a completed weld?
One might expect a higher "D" of the TMCP steels to enable weld hydrogen to disperse more rapidly, lowering peak hydrogen concentrations more rapidly, reducing susceptibility to delayed hydrogen cracking of the weld.
Please suspend judgement on this issue for a while - for reasons which will become apparent.

The human story in the University

It was not a happy time in this "restarted" experimental stage.

For me, there was a huge amount of preparation for the refined more commercial weld-tests of the further "WWHP" test series. I worked and worked, with results seeming far away and time to produce valuable results being in limited supply.
Most of my experimental investigation time was spent in a boiler-suit in the machine-shop, with my toolchest beside me, maintaining and operating machine-tools to cut and machine plate steel samples for the tests.
The strain on me of working for a high-stakes event some time in the future was indeed a strain.

My supervisor was still unrecoverable and out-of-action.

A provisional plan of the way forward with a series of staged achievable goals had been drawn-up immediately after "the big meeting" where "the miscreance" was uncovered. The Department and my interests had complete alignment in wanting a successful project outcome.
Having achieved the first stage of the plan, I went up to the Head of Department's office, where his personal assistant booked me in for a 10-minute meeting when I requested a 2-minute meeting.
I duly arrived at the appointed time and was indicated to go in.

I apologetically offered that I had passed the first goal of the plan, whose formulation now lay a while ago. Seemingly not much to report as I felt, but it was something.

I was forcefully questioned "Is that what you came to tell me?". Standing my ground, I replied "Yes, that's right. That is the progress so far". Again questioned with a forceful tone of query "Nothing else?". My reply "No, just this".

The next moment was to completely invert my world.

This "figure of authority" started waving his arms around almost shouting "I can't believe it! That's the first time some has come through THAT DOOR" (sweeping arm gesture) "to tell me GOOD NEWS!!!".

Sinking back in his chair he lamented "People come to me. They've had an argument. They want ME!!! to sort it out!!!". "I achieve so little in a day."
Further reclining into his large leather-upholstered swivel chair, looking very human, he relaxed into a conversation tone continuing "At least a prisoner sentenced to break rocks on Dartmoor knows how long that sentence is!". (Explanation: "Dartmoor" is a notorious hard-labour prison for tough criminals).

I was having a feeling of a transformational moment reaching a vanishing point at the top of a scale, then to emerge in a mirror-image inverse space on the other side of the singularity, from which I could proceed on upwards in my new environment.

I had moved on to a different space...
It had been noted that I will deal myself with unfortunate situations, but however forceful I needed to be I never overstepped what was absolutely necessary to push things back onto "the centre-line".
I lamented the situation with my supervisor, but my own abilities did not provide a way to remedy the situation. Nor did I have a "magic wand" to achieve the same remedy.
I was finding that I was having private conversations of the character
"I anticipate that in about two weeks hence {this person} will come to you with an allegation which sounds like {whatever}. In that situation, I" (hand-gesturing towards myself) "do not need you to do anything".

In an academic world, I was allowed a lot of autonomy to get on with things as I saw fit. Which was very fortunate as I navigated the challenges, revealing little of my intentions.

The human story of other interactions

The sponsoring company was now out of the picture. No more funding was forthcoming from them. We had no desire for the "product" their previous contact with us offered.

Actually within the University, but put in "other" because I kept it very secret, was that an academic in the Department had taken an interest in my work. This very intellectual man, who had come to Britain as a refugee, had devoted his career to diffusion of solutes in polymers. For which there was strong experimental evidence that they behaved in no way like "Fick's Model" (and Fick would not have been at all upset, as he was clearly a perceptive person who well knew the limitations of that model). So my novel findings for metallic systems were of interest. Particularly the suspicion of "asymmetric diffusion". Where some investigations show hydrogen enters samples exactly as Fickian kinetics would anticipate, but leave at some slower rate which is also qualitatively different.
Given the tense situation, I ensured no-one saw me entering or leaving the guy's office. When there, we discussed science and diffusion for many hours.
The reason for the confidentiality was to avoid him being targetted in the continuingly tense atmosphere in the Department.

Elsewhere in the world, I was visiting then British Steel's research laboratories in Rotherham.
They were doing a lot of work investigating the resistance of plate steels to "sour" crude-oil, in relation to manufacturing line-pipe for oil-industry applications.
That is a hydrogen phenomenon. Where the hydrogen source is chemical, from the combination in the oil of acidity and hydrogen sulphide acting in some way as an entry-promoter. An infinite source, as long as the oil flows. Which can "tear" steels to fractured shreds.
We were both considering hydrogen in solution in steel, but our objectives were different - welds and weldability vs pipelines and sour-oil resistance. Hence no "toe-treading" in openly sharing information.
They gave me plenty of good hints and I was able to give them warnings of things which mattered to them where I had found that hydrogen behaviour is not as described in text-books and most scientific literature.

Also at the University, in the Department of Mathematics and Computer Science some of the lecturers were very indulgent of my simple / simplistic questions. Mainly then about mathematics, but later about computational matters. Their beneficial influence was to feature majorly imminently.

Some "clear-up" experiments

I had a suspicion that regarding "D" in steels that the main explanation was whether the steel had "pearlite" , or pearlite was "extinct" in the microstructure by reason of the lean composition and refinement of TMCP steels.
The reason for the simplicity would be

I've glossed-over one point - the "9590" steel (name has no meaning; it's a batch-number) which you will find on searching the results - is actually an "intermediate-generation" TMCR (Thermo-Mechanically Controlled-Rolled) steel, with a lean composition but still higher carbon level than the most developed TMCP steels - plus it lacked the accelerated-cool of TMCP steels. It has dark areas in about the right proportion to its carbon content - but they are too fine to resolve with optical microscopy (which is limited by physics to maximum 2000X magnification; in practice 1000X magnification for common laboratory metallurgical microscopes).
Its "D" fits with the "with pearlite" higher-carbon steels.

With no budget left, I was "slipped" an hour of scanning electron microscope time to go searching for pearlite where optical microscopy doesn't see it.
The dark areas in the "9590" steel resolved as being very fine pearlite by scanning electron microscopy.
I also got my "newest variant" TMCP steels into the microscope in that time-slot. The miniscular volume-fraction of small dark "lumps" we could see at that high magnification we chased further to even higher magnifications, concluding they are the various very fine homogenous precipitates expected. Zero pearlite, which was completely extinct in the TMCP steel microstructures.

Many thanks people...

My impression of pearlite or no-pearlite as the arbiter of "D" low or high, respectively, was supported. Though not proven - you would need a bigger appropriate set of independent samples to "conclude".

Comparing two main types of research project

My endeavours entitled me to make this point.
There are two main types of research project, producing two different types of scientist.

Generally the "join an established research group" student would be more intellectual. The student conducting the specific objective applied research would be a more practically-minded independent person.

My project and who I am fit the latter category.

The stretching time-frame

I had a problem of interpretting my data. To be frank, things did not look good. All I could do was try writing-up what I had; but I had a sick feeling it would not end well. Two years...


The folk at the Department of Mathematics and Computer Science have received passing mention.

Without a brilliant school background as a child, mathematical solutions to quantitatively predict what you would expect diffusive outcomes to be, according to current "Fick's 2nd Law" theory, never seemed to get any closer. Explanations flew past me.

I was also grimly aware that I would need a full 3-dimensional solution to interpret my experiment. 1-dimensional solutions (eg only the thickness dimension varies) are difficult enough.

An entirely different style of teaching laid a necessary precursor.
Observed applying simple computer programs to calculate areas of weld-beads from x, y outline coordinate data points, eg thesis Figure 3.4 on page 117, a friend asked me to write for him a program which integrated "y=x^2" (y equals x-squared) from 0 to 1, by the same summation method, but with the "height" "y" given by calculation from that local "strip's" value of "x".
His purpose was unknown to me, as the answer can readily be obtained by most technical, scientific and mathematical people, by mental-arithmetic in a few seconds maximum, as 1/3 exactly.
Done and offered him, he changed at the core of the small program the "y=x^2" line to a more complicated mathematical expression, instructed "run", and declared "That is the Error Function".
(see thesis Figure 2.1 and associated explanation on page 49)

I convulsively rose out of the chair gripping its arms crying out "WHAT?!!!!", realising that in one "stroke" that this fellow had laid out naked to me the full mechanism of computational solving "awkward" mathematical expressions. He explained for example that the "Error Function" has no known "arithmetic" "on-paper" mathematical solution. The simplicity, which no explanation had previously suggested, left me astonished.

The "thinking" percolated its way into my mind, in its own time.

That torrentially rainy afternoon offered no premonition of the miracle about to occur.

Between starting to sit down in an armchair and landing seated on the armchair, a solution which would predict the quantitative outcome of applying Fick's 2nd Law to diffusive situation came to me.
This can't be real, surely?
A new, previously unsuspected solution for Fickian diffusion?!
(mathematicians later told me, when I demonstrated how the method worked two years later, that solutions of this type did exist, so "novelty" is not a claim which should be made).

The surreal aspect of the solution as it came to me was its incredible simplicity. Wherever height "the bar" was set, no position could be too low that this solution wouldn't go straight underneath it.

The "1/6th-jumping" solution is described in thesis Section 2.4 starting on page 64, with first illustration Figure 2.11 on page 65 followed by other illustrations explaining the method.

Before making any further pronouncements, I had to verify that the solution worked. It could be tested for a one-dimensional situation by shuffling around small squares of paper each representing a quantity of solute. I must have been quite a sight, there sitting at tables in public places, earnestly sliding around pieces of paper, in line with the working of the algorithm, following a mission known only to myself.
It did appear to work in the way intended, from the outcome of the paper-shuffling.

My solution was inherently 3-dimensional, but could be restricted to two or one dimension if desired. Could I really have found a way to compute what my samples would do if "Fickian" behaviour were true?
If so, that gave me a hypothesis to test: "Hydrogen movement in a weld is Fickian diffusion". Which would be "accepted" or "rejected" on the basis of comparing the experimental result to the computed result.
That would definitely get me my Doctorate, as beyond any doubt the experiments were good.

Getting a version of "BASIC" installed on my computer, I quickly managed to code a one-dimensional implementation of my algorithm. Defining a situation matching "the infinite body solution" - a particular simple case where an on-paper mathematical solution is known given use of tabulated values of "the Error Function" - the computed outcome matched the on-paper solution.
(see thesis Figure 2.21 on page 76)
A 1-dimensional mathematical solution to a situation approximating a weld on a plate had been achieved (Coe and Chano, 1975) and my solution defining the same situation gave identically the same outcome.
So empirical evidence was that my algorithm works - rather well.

Getting this far, in something like 2 to 4 weeks, had already introduced me to some computational concepts, and I could see that implementing the algorithm in 3 dimensions would require a lot of computing power.

Heading to The Department of Mathematics and Computer Science, one of the Mathematics lecturers took me and introduced me to the Department's two technical staff members who advise-upon and administrate the Departments supercomputing needs.

It was immediately confirmed that my application did fall in the domain of "supercomputing". Also that I could have obtained for me time on a supercomputer at one of the National laboratories, on their say-so that the objective was worth having and the algorithm worked correctly as best they knew.
It was later to transpire that I managed all computations on a tuned-up "Personal Computer" - but the good though and the assurance there was a path ahead was my "Green light to Go".

In the University library I found a very artistic book about supercomputing, and its cover-page showed the painting The Great Wave off Kanagawa morphing left-to-right from the painting on one side to a discretised computational model representation on the other side. Although purely artistic imagination, the scientific concept was there - would the physics of water, wind, the presence of the sea-bed and other factors interacting lead to a prediction that "The Great Wave off Kanagawa" would be qualitatively predicted by known Laws of the Universe?
Further in, the book showed that with the coming of the Cray-2 supercomputer in 1985, it became possible to show that the Laws of Physics applied to the atmosphere did lead to a prediction of exactly what is seen in a "hammerhead" thundercloud and its storm.

"Supercomputing" in science and engineering is generally, as in this case, about representing the real situation with a "parallel Universe in numbers" of physical laws represented as mathematical expressions, "loaded" with the "starting values" from which the outcome will evolve as the mathematics progresses. An activity known as "number-crunching".

This is all fanciful in terms of my incredibly simple algorithm, but did give some idea of the area of endeavour I needed to enter to obtain my Doctorate.

I could see that the computation would require much more computer memory that was then familiar on "personal computers" and take some time to complete - minutes, hours or days.

I would have to learn and write in a computer-programming language used on supercomputers ("C" and "Fortran").
After some consultation I committed to going with "C".

Another fortunate turn of events occurred. The unix-family operating system had been "ported" to common "PC" personal computers - like mine - by the "Linux" project.

The "office applications" operating systems of the day were way too fragile to cope with someone computer-programming. Any one mistake, of which you make squillions, and there's nothing left operating on the computer. Nothing left to ask what went wrong. The fans are whirring and the "power on" indicator lights are on, but there's nothing left surviving running on the processor.
"Linux" made the personal computer ("PC") with its operating system as solid as The Rock of Gibraltar. For sure its then mainly command-line interface lacked "office user" appeal - but that was far less than irrelevant for my endeavour.

A little bit of fiddling with my toolkit had a separate "hard-drive" for the Linux system installed, so I could "boot" the computer to either an office system or the Linux system, as I chose for my work.

I set about designing then encoding my algorithm and reappeared 2 months later, with some of its early stages written and doing something apparently as-intended.
The initial response from one of the computational mathematics research students was quite a pause, then a comment "I wouldn't have used so many 'pointers'". She showed me the one case she would use them. My algorithm so far was about 80% 'pointer' operations(!).
Taking an analogy - it was is if a trainee pilot was instructed about the importance of flying low, then the importance of flying fast, and sent off on a one-hour first training flight had come back half an hour later, with smoke coming off the aeroplane, twigs and leaves stuck in various places and a dawning realisation that the student had just flown both supersonic-fast and at treetop-height.
'Pointers' are an expression in the "C" language which is only one step of abstraction above directly-addressed computer-memory access. I'd chosen this form of expression after realising that for the algorithm to run fast, which it would need to be to get through a 3-dimensional computation, I needed to be very much aware of schematically how a computer (of that generation) worked internally. (very specifically: ensuring huge sequences of variables would be found in the "on-chip cache", minimising "fetches" from the main "RAM-bank" memory-chips). In order to efficiently transfer variables in and out of the computer's memory surrounding the computational stage.
There were other "coding" features designed to make the algorithm run fast as-written. I "coded" it to minimise "branching" decisions, in making crucial variable-handling "working tips" of the program coded-up as large amounts of linear nearly identical code, each very carefully tested for correctness, and a log of the size dimensions of the solution enabled the solution to run "flat-out" "blind" through long uninterrupted volumes of the represented sample.

I was being made very welcome within The Department of Mathematics and Computer Science. I was stumbling across many practicalities of computing which they confirmed are very much known to be the case.

It worked!
Set to solve for a sphere, the answers matched the on-paper solution (on-paper, a sphere can be reduced to one dimension (radius), enabling the on-paper mathematical expression.
Every other solution was "reasonable".
"Reducing" the solution by making everything "equal-and-opposite" in two of the dimensions, the algorithm matched the known one-dimensional planar on-paper mathematical solutions.

I quickly set-up solution for weld samples - the "shapes" with numbers representing the initial hydrogen concentration - and it started producing answers.
Typically from pressing the "Enter" key for the instruction to set the computation going, until the computation reached the finishing condition (eg only a 200th part of the original solute remains in the body - a negligible amount which cannot change the overall outcome revealed whatever were done with that "residual" quantity), the computer would run for several hours.

Over at The Department of Mathematics and Computer Science, there was interest as it was possible to accurately deduce the real the speed of a "PC" personal computer, in "megaflops", from how fast my algorithm ran. That was because it was so clear how many mathematical operations were needed to "go around my solution once" that one could easily tally how many mathematical operations were performed in one second (for what it's worth, in 1997, my 1995 computer was managing 3.5megaflops (millions of floating-point mathematical calculations per second).
No commercial information could be trusted to truthfully report this figure, and revealing it by tests isn't easy. The simplicity of my algorithm did expose this performance value of the computer.

With run-times of a few hours maximum, there was no need to get access to a supercomputer.
The longest run "batched" a lot of computations to represent the "WWHP" test, and ran for 170 hours. With that being predicted, it gave me my first absolved time-off for a long time.

To me, all this effort was in the service of metallurgy and welding. My single purpose as a practical scientist coming from the steelworks was to find an answer to: is the observed behaviour of a weld "expected" according to assumed theory?
That purpose took me down a straight-and-narrow path in computing, with little knowledge gained of what lay around that path - but the distance I travelled in that narrow endeavour was considered notable.

How I applied my computational solution

Reminder of what a computational solution gives us

As previously mentioned, the computational solutions enable me to test the hypothesis "Hydrogen movement in a weld is Fickian diffusion".
The computational model creates a virtual world in which "Fickian diffusion" is exactly what happens.
So you compare the computational model's outcome to the experimental outcome. It they match, it looks to be correct that hydrogen movement in a weld is fully described by "Fickian diffusion".
If they are incompatibly different, it would appear that hydrogen movement in a weld is controlled at least partly, if not totally, in some other way.

The original objective - should so much hydrogen be appearing distant to the weld?

There were two experiments I wanted to model, which had driven all this computing activity

The answer emerged clearly:
"too much" hydrogen emerges from surfaces distant to the weld deposit for "Fickian diffusion" to be the complete explanation of how hydrogen moves around in a weld.

For the Christensen and Evans experiment, that's more than twice what "Fickian diffusion" "expects". That looks to be how things happened for every hydrogen-containing weld ever made.
For the "WWHP" test, it actually proved that those early high-hydrogen welds "should have" "pushed" hydrogen through the full 15mm thickness. However, for the low-hydrogen R-FCAW series, the hydrogen should have "struggled to a final stop" by 9mm thickness - whereas the hydrogen "joyfully" races through the full 15mm thickness.

A hilarious finding is generated for my "WWHP" test by these investigations.
Those clear values of "D" for each steel, coming from those long linear "x vs root-t" plots, apparently shouting-out "Fickian behaviour", should not be possible according to this "100% Fickian diffusion" model!
The same physical effects will surely be happening to just about every other experiment ever performed to measure "D", so "my" values of "D" are overwhelming likely equivalent-to and equally as valid as all other measurements of "D".

The other findings - the incredible "bounty"

The experimental programme had shown interesting results, and significantly increased knowledge on weld hydrogen distribution and movement in welds.
However, it hadn't answered the question driving the creation of this project: why do the TMCP steels have such good weldability compared to the "classical" plate steels?

The computational modelling programme changed that. Pursuing the "quantities" question, it thrust before me a completely unexpected "within the weld-zone" behaviour. This not only explained the weldability issue but also seemed to explain the "sour-oil" issue for oil-industry linepipe.
Also landing me into some "human" problems, as the fundamental physical explanation was to some "unacceptable" by reason of being taken as a "scientific heresy".

Representing different "D"'s in one modelled object can be and was done by the "1/6th-jumping" method by making the lower-"D" material jump less than 1/6th. For instance, to have half the diffusion-coefficient, you jumped 1/12th out of each cube-face, and retained 6/12ths, ie at half, in that cube.
In serving the "quantities" question.

Run that computational model for a weldment comprising a weld-metal and a plate-metal of different properties, and the hydrogen concentration profile has an abrupt step-change at the "fusion-boundary" between weld-metal and plate-metal. See for example thesis Figure 4.22 on page 191.

Then you realise - that has to be physically correct!
That is the advantage of all modelling activity - it is a structured activity for focussing the mind, from the most general matters to the finest detail, which can uncover what prove to be the most important crucially relevant questions. Which then lead to the important answers.

Here had to be the answer why TMCP steels have weldability so incredibly good, above the benefit expected from lean composition alone!!!
At last - success!!!

That step-concentration change at the fusion boundary, a sheer drop from the weld-metal to the plate-metal side, is giving relief from hydrogen embrittlement right where it is most needed, at the heat-damaged "Heat Affected Zone" (HAZ) of the plate metal immediately adjacent to and up to the weld metal.

Here comes the "scientific heresy", offending many and producing such eruptions of aggressive behaviour in some that I had to be very careful not to assert this point.

Considering physical fundamentals; that implies both diffusivity "D" and solubility "S" must be dependent variables on the single independent variable of the state-of-solution - and that "D" and "S" tend to be inversely related.
Thus, for a given material and solute, if something done to the material causes for the solute the diffusivity "D" to halve, the solubility "S" will double.

When as a scientist you look around, you realise there's information demonstrating that is the case. Sometimes exactly so for some systems. An exactly-so case for steels is cold-deforming ("cold-working", eg "drawing") the steel, where "the D S product" remains absolutely constant while D decreases and S increases with increasing cold-deformation. There are other cases described in my Thesis.
These data were there but the interpretation seems to never have been spotted.

What is taught in a first Degree (Bachelor's Degree) at a University "prohibits" this from being so, as, using economical language and creating a manageable "story", it is taught that Fick's Laws quantify the movement of a solute in a solvent.
Every teaching and impression given has diffusivity "D" and solubility "S" as independent (not connected) variables.
Hence the "angry aggressive, 'this is heresy!'" response from those with a coaching in technical knowledge who have not gained the adaptability of scientific thinking.

The realisation that diffusivity "D" and solubility "S" for hydrogen will be at least approximately inversely proportional across various steels has important ramifications.
So TMCP steels with a high "D" must have a low "S". If only we had a premonition of the later importance of the issue! To persist and overcome difficulties in trying to measure "S". But that's the "rough-and-tumble" world of applied science we have to cope with.

Firstly, for welds we can conjure up a picture for TMCP steels of

Which is good.
Next comes the realisation of huge commercial consequence, and amazing unexpected scientific good fortune.

An at-least approximately inverse proportionality between "D" and "S" for hydrogen in steels explains the "sour-oil" (acidic sulphurous crude-oil) resistance of TMCP steels!!!
Giving answers regarding the issue of what can we do about imported TMCP steel plates having to be put through British pipe-mills while British plate-making capacity stands idle.
Taking a wider global view, an ability to explain sour-oil resistance of steels affects a market in millions of tonnes of steel per year.

Let us loop around a more expansive view of what is meant by "solubility".

It seems likely that, comparing the "classic" plate steel to a TMCP steel when both are containing a flow of the same "sour" crude oil, the TMCP steel will absorb less concentration of hydrogen at its inner surface, and disperse it away from the pipe outer surface more readily given the favourable "D". Do remember though that we must look "below" "D" and "S" to that single concept "the state of solution of hydrogen in the steel".
As TMCP steels have a "clean" homogenous microstructure of ferrite grains with no second-phases, it is likely that the hydrogen derived from the oil (we are not talking about weld hydrogen here!) does not locally accumulate anywhere to initiate a localised damage mechanism - which can then propagate as gross damage in extended time.
The "classic" steels do have extensive second-phase of pearlite; and the distribution of that pearlite is usually visibly inhomogenous, seen by metallography and microscopy and known as "banding". Suggesting some locations may be particularly susceptible to hydrogen damage.
This is mainly "hand-waving" speculation.
The issue of "D" and "S" is demonstrated and looks overwhelmingly likely to offer the explanation in some way.

How absolutely amazing! From our interesting experimental results, our computer-modelling, performed as a metallurgist interested in scientific outcomes, has enabled scientific and commercially-useful findings to be extracted. Extremely commercially valuable they are!

"Writing-up" and finishing my Doctoral work

My supervisor, who I had seen little of for a long time, officially retired. I received a very surprised phone call from the materials department of the University, asking if I knew one of their other academics, who had walked into the Departmental office and offered to take-over as supervisor of my project.
This was the academic I mentioned previously, who had a big interest in diffusion in polymers, with whom it seemed my extensive discussions had been kept more secret than I had realised.
The Department was contemplating having to declare abandonment of my project, as they had no-one else with any expertise in my area of investigation.
Such are the way events can hurtle along.

Two Universities and three supervisors was thought win the unfortunate record for most mayhem and carnage related to one PhD research project.

A complete digression. A story I can tell, given decades gone by. An academic told me of one of his students, who finished his PhD quickly with well-liked outcome. Earlier, the more senior co-supervisor had declared himself not happy with the project and stated he recommended it be terminated. That night, the co-supervisor died of a heart-attack which struck with no prior health warning. In the morning, summoning his student and conveying the news, he surmised that the co-supervisor had probably not told anyone of his decision, as the meeting was in the late afternoon. Intending to make his report in the morning. Had the University come to know of the decision, they would have "honoured" it. The student and the supervisor kept silent. The supervisor submitted his own favourable appraisal. The project ran to a very successful completion.
Such was the environment I was inhabiting in those years.

With a good body of knowledge, I wrote "like mad".

Slight problem. I had little-enough explained my experimental findings to anyone. I had never explained to anyone how my computational model worked, despite using it for more than two years and discussing with my new, final, supervisor what I might do with it which would be useful.
It took me 20 minutes to find an explanation which conveyed how it worked.
He looked up from the sketch to me and asked "So if Adolf Fick had had an automatic computer, he would have probably solved his model in this this way?", to which I replied "Yes".
(To a scientist solving mathematical and modelistic challenges, "a computer" in common language is "an automatic computer" - it is a machine which automatically proceeds though mathematical and logical steps to a computed outcome)

A favour had to be "pulled" to get an eminent academic at another University to be the External Examiner for my first Doctoral "viva" ("viva voce" - Web-search description if interested).
That academic quickly changed to realising there was something valuable here; but equally, this was the first time anyone but myself and my final supervisor had known anything of my work. Hence, I had to re-write large sections of my thesis responding to notes very reasonably requiring better explanation.

Reconvening, the atmosphere was totally different. The External Examiner took the lead, explaining the most important duties for both himself and the Internal Examiner, the previous Head of Department when I came to the University, were "long-stops" like: is the really work my own?
Referring to the substance of my Thesis, he swept his had in easy gestures as he summarised the two "legs" on which the work stood - the good body of experimental findings, then the computational work. Which he commended with "where we can actually see what it is that you have computed". My "Unsuccessful Experiments" section got a favourable mention as showing the range of efforts made in the course of getting to these findings.

A few question-and-answers later - including very carefully side-stepping the question of "is diffusion Fickian?" with a non-committal comment on inconclusive evidence and nothing could be said without more research - and it was declared that I had done a model piece of investigation and a model thesis, and that concluded matters with a clear "pass".


The finding from my work for the British steel industry regarding plate steel production was something like "You're s****ed". There was no way to get TMCP steel advantages without TMCP steel microstructure. Not going to happen in Britain, hence no dominating advantage coercing a British steelmaking company to recruit me.
Meanwhile, German and Japanese steelmakers had a well-established industry and environment for making TMCP steels.

I had research ideas for continued consolidating progress, but apart from the likelihood of success gaining funding, after this experience it seemed the last thing I needed now, as a person, was to remain in academia.

I went forward with an onward path which would prove to be "interesting". How could it follow after this experience that one could disappear into a comfortable obscurity? That destiny isn't reserved for people who have an abnormal lurid background :-)

(R. Smith, 23Feb2017, 24May2017)